{"paper":{"title":"Counting Houses of Pareto Optimal Matchings in the House Allocation Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM","cs.GT"],"primary_cat":"math.CO","authors_text":"Andrei Asinowski, Bal\\'azs Keszegh, Tillmann Miltzow","submitted_at":"2014-01-21T15:44:22Z","abstract_excerpt":"Let $A,B$ with $|A| = m$ and $|B| = n\\ge m$ be two sets. We assume that every element $a\\in A$ has a reference list over all elements from $B$. We call an injective mapping $\\tau$ from $A$ to $B$ a matching. A blocking coalition of $\\tau$ is a subset $A'$ of $A$ such that there exists a matching $\\tau'$ that differs from $\\tau$ only on elements of $A'$, and every element of $A'$ improves in $\\tau'$, compared to $\\tau$ according to its preference list. If there exists no blocking coalition, we call the matching $\\tau$ an exchange stable matching (ESM). An element $b\\in B$ is reachable if there "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5354","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}